Vortex sheet approximation of boundary layers

Abstract

0Running head vortex sheet approximation · Abstract A grid free method for approximating incompressible boundary layers is introduced. The computational elements are segments of vortex sheets.The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier vortex method • . The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder-piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms.

Vortex penalization method for bluff body flows

“…It is therefore important to capture in an accurate way vorticity boundary conditions. In classical implementations of vortex methods, the no-slip boundary condition is satisfied through the creation of vortex elements [16][17][18] or by updating particle strength to account for vorticity fluxes at the boundary [2,4,7]. The no-through flow boundary conditions are implemented together with the Poisson equation to determine stream functions and potential in (5).…”

“…In this section, periodic boundary conditions on the box boundary D were prescribed for system (17). A correction of the velocity field was performed at each time step in order to satisfy free stream velocity u 1 D .u 1 ; 0/ D .1; 0/ imposed at the inlet.…”

Parallel Scientific Computation

“…For example, simulations of systems of gravitationally interacting masses (25), electrostatically interacting charges (26), or vortices in an incompressible fluid (27) involve what is known as the N-body problem, in which every particle must interact with every other one in the system.…”

An investigation of random choice method for three-dimensional steady supersonic flows

“…Recently, the idea of random choice by Glimm has been extended and used in a broad way, e.g. in the vortex method [11] and the front tracking method [12].…”